2x^4+x^3+5x^2=0

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Solution for 2x^4+x^3+5x^2=0 equation: 


Simplifying
2x4 + x3 + 5x2 = 0

Reorder the terms:
5x2 + x3 + 2x4 = 0

Solving
5x2 + x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(5 + x + 2x2) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(5 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + x + 2x2 = 0

Solving
5 + x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
2.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 0.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 0.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 0.5x + x2 = 0 + -2.5
0.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
0.5x + x2 = -2.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = -2.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + 0.5x + x2 = -2.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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